A ball A is thrown vertically upward from the top of a 30...

A ball $A$ is thrown vertically upward from the top of a 30 -m-high building with an initial velocity of $5 \mathrm{m} / \mathrm{s}$. At the same instant another ball $B$ is thrown upward from the ground with an initial velocity of $20 \mathrm{m} / \mathrm{s}$. Determine the height from the ground and the time at which they pass.

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Key Concepts

Equating Motion Equations for Interception

In problems where two objects are moving along the same line, setting their displacement equations equal to each other helps determine the time and position at which they meet. This method involves solving simultaneous equations derived from their respective kinematic formulas.

Gravitational Acceleration

This constant, usually approximated as 9.8 m/s² near the surface of the Earth, is the acceleration due to gravity that acts downward on all objects. It is a central factor in determining the trajectory and time of flight of objects in free-fall or upward motion.

Projectile Motion

This is the study of objects launched into the air where the only force acting on them is gravity. Projectile motion is typically broken down into vertical and horizontal components, with the vertical motion influenced by gravitational acceleration.

Kinematic Equations

These are mathematical equations that describe the motion of objects under constant acceleration. They relate displacement, initial velocity, acceleration, and time, allowing one to predict future positions and velocities. In vertical motion problems, they are used to model the motion of objects subject to gravity.

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